Problem: Simplify the following expression: $q = \dfrac{1}{8k} - \dfrac{4}{7k}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $8k$ and $7k$ $\lcm(8k, 7k) = 56k$ $ q = \dfrac{7}{7} \cdot \dfrac{1}{8k} - \dfrac{8}{8} \cdot \dfrac{4}{7k} $ $q = \dfrac{7}{56k} - \dfrac{32}{56k}$ $q = \dfrac{7 -32}{56k}$ $q = \dfrac{-25}{56k}$